While MNA (and also MLA) naturally gives a DAE of port-Hamiltonian structure, see e.g. [1]}, [2]} for related results, simple examples show that the resulting DAE need not be SA-amenable, see [3]}.
In [3]} a branch-oriented model in port-Hamiltonian form based on a normal tree is presented that is closely related to the results presented here, but uses different variables.
A different definition for port-Hamiltonian descriptor systems is given in [5]}, [6]}.
With a slight increase in the dimension of the system
– by adding the variables \(\iota _{\hspace{0.2pt}\texttt {C}}\) , \(\nu _{\hspace{0.2pt}\texttt {l}}\)  and the corresponding relations \(\nu _{\hspace{0.2pt}\texttt {l}}=\dot{\varphi }_{\hspace{0.2pt}\texttt {l}}\) , \(\iota _{\hspace{0.2pt}\texttt {C}}=\dot{q}_{\hspace{0.2pt}\texttt {C}}\)  – our formulation can be transformed into this form.
Due to (A3) \(n_{\hspace{0.2pt}\texttt {l}}\)  and \(n_{\hspace{0.2pt}\texttt {C}}\)  are usually small.
The MNA formulation is based on Kirchhoff's laws written as
\(\nu = \widetilde{A}^\quad \text{ and}\quad \widetilde{A}\iota = 0,\) 
